1. Field
The present disclosure relates generally to methods and apparatus for QAM modulation, and more specifically to QAM modulation of signals using a pair of constant envelope polar modulated phasors that afford more efficient power amplification of the signals.
2. Background
In communication systems, whether in wired or wireless communication systems, data symbols are conveyed on carrier signals by modulating the signals using various modulation schemes. One such known scheme is Quadrature Amplitude Modulation (QAM). In QAM, a mapped symbol is defined by two orthogonal voltages defined as the in phase (I) and quadrature (Q) voltages. The number of bits representing each symbol at I and Q for a square constellation of defined I, Q points is given by:N=log2√{square root over (QAM_Size)}  (1)where QAM_Size is the constellation size such as 4, 16, 64, 256 QAM etc., and N is the number of bits for I and for Q. For example, a QAM_Size=64 would yield N=3=log2√{square root over (64)} thus overall 6 bits 3 for I and 3 for Q.
Consequently, each point in an I/Q plane can be described by two sets of orthogonal voltages. In other words, the equivalent vector is the sum of two orthogonal vectors that are varying in time. The equivalent vector R(t) is given by:R(t)=√{square root over (I(t)2+Q(t)2)}{square root over (I(t)2+Q(t)2)}  (2)where the phase φ(t) is given by
                              ϕ          ⁡                      (            t            )                          =                                            tan                              -                1                                      ⁡                          (                                                Q                  ⁡                                      (                    t                    )                                                                    I                  ⁡                                      (                    t                    )                                                              )                                .                                    (        3        )            
Accordingly, representing the vector in complex domain I and Q projections is given by:
                    {                                                                              I                  ⁡                                      (                    t                    )                                                  =                                  Re                  ⁢                                      {                                                                  R                        ⁡                                                  (                          t                          )                                                                    ⁢                                              exp                        ⁡                                                  (                                                      j                            ⁢                                                                                                                  ⁢                                                          ϕ                              ⁡                                                              (                                t                                )                                                                                                              )                                                                                      }                                                                                                                                            Q                  ⁡                                      (                    t                    )                                                  =                                  Im                  ⁢                                      {                                                                  R                        ⁡                                                  (                          t                          )                                                                    ⁢                                              exp                        ⁡                                                  (                                                      jϕ                            ⁡                                                          (                              t                              )                                                                                )                                                                                      }                                                                                                          (        4        )            
Consequently, the equivalent vector varies in both amplitude and phase. In this manner it describes various symbols of a constellation of symbols at various times based on the I and Q values. When amplifying a non-constant envelope signal (i.e., a signal having varied amplitudes) by a power amplifier (PA), the amplification is associated with amplitude changes. A QAM signal, however, is associated not just with amplitude changes, but with phase changes as well, which may result in distortion when amplified by the PA. The amplitude change in a PA is associated with AM modulation. Hence, in transmitters, a PA has to be designed with high linearity and back-off in order to prevent distortions and spectral regrowth. Consequently, such amplifiers generally operate in a highly linear mode, such as a Class A amplifier for example, which results in low efficiency operation of the amplifier. Accordingly, there exists a need for developing a scheme for QAM modulation affording increased efficiency operation for a PA in a transceiver.